Goals from James Morrison and Kenny Miller gave Scotland a 2-1 lead in their friendly against England at Wembley but second-half goals from Manchester United's Danny Welbeck and Southampton's Rickie Lambert saw Roy Hodgson's side emerge 3-2 winners in the match to celebrate the 150th anniversary of the Football Association.
Strachan admitted he had not felt as disappointed in years, despite a hugely impressive performance from a Scotland side who defeated Croatia away in June.
"I probably will be encouraged in a couple of days but right now I don't feel encouraged," said Strachan.
"I feel huge disappointment for everybody. It could have been a result you'd be talking about in 40 years' time.
"I discount the last 20 minutes when we were trying everything, throwing everything left, right and centre, it got a bit disorganised then.
"We were trying to protect a few players because I didn't want to send them back to their clubs with groin strains or hamstring strains. When we lost a couple of our more experienced players the game went away from us.
"James Forrest did a lot of good things but we had to protect him as well."
Strachan put England's second-half goals, both headers, one from a free-kick and the other from a corner, down to defensive lapses.
"There are things I liked but our concentration went at times," Strachan said. "That was the defining thing. It wasn't work rate, it was concentration that cost us.
"You have to give them credit for putting the ball in the right place at the right time. I go back to when Manchester United won in 1999 and Beckham in the 90th and 92nd minutes produces crosses which are telling.
"People think it is easy to take free-kicks and corner kicks, it's not. Everybody's watching and to be able to deliver it and strong enough to head it, you have got to give them credit for that.
"There were so many players coming on and off at that point it was a problem."
At least Strachan knows he has much to work with, despite his side being unable to qualify for the World Cup.
"When it went to 2-1 I genuinely thought we were going to win the game," said Strachan. "I will feel better hopefully in a day or two but at the moment I'm not enjoying the experience.
"I forgot this was a friendly. It doesn't feel like that now. It's a long time since I've felt as bad as this."